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# Using Algebra in Statistics and Probability Practice Questions (page 2)

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#### Practice 2

 1. The probability of selecting a spade is . This probability is equal to the number of spades, 9, divided by the total number of cards. We are looking for the number of diamonds, so let x represent the number of diamonds. The total number of cards is equal to 7 + 9 + 11 + x = 27 + x. The probability of selecting a spade is . Set equal to . Cross multiply and set the products equal to each other: 3(27 + x) = 99 81 + 3x = 99 3x = 18 x = 6 There are 6 diamonds in the deck. 2. The probability of selecting a baseball is equal to the number of baseballs divided by the total number of balls. Let x represent the number of baseballs added to the sack. There are now 4 + x baseballs, and 4 + x + 5 + 6 = 15 + x total balls. The probability of selecting a baseball is equal to . The value of x will make this probability equal to , so set the two fractions equal to each other, cross multiply, and solve for x: 4(4 + x) = 3(15 + x) 16 + 4x = 45 + 3x 16 + x = 45 x = 29 For the probability of selecting a baseball to become 29 baseballs must be added to the sack. 3. The probability of selecting a nickel is equal to the number of nickels divided by the total number of coins. Let x represent the number of nickels removed from the jar. There are now 16 – x nickels, and 14 + 16 – x + 6 + 12 = 48 – x total coins. The probability of selecting a nickel is equal to . The value of x will make this probability equal to , so set the two fractions equal to each other, cross multiply, and solve for x: 48 – x = 5(16 – x) 48 – x = 80 – 5x 48 + 4x = 80 4x = 32 x = 8 For the probability of selecting a nickel to become , 8 nickels must be removed from the jar.

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